P and q compound statements

Give that p and q each represent a simple statement, write the indicated compound statement in its symbolic form.

1.p: This is a hammer
q: This is a tool.
If this is not a hammer , then this is not a tool.

2. p: The cone has three scoops .
q. The cone costs $1.85.
The cone has three scoops if and only if the cone costs $1.85.

3. p: The cone has three scoops.
q: The cone costs $1.85.
The cone does not have three scoops if and only if the cone does not cost $1.85.

4. p: The outside humidity is low.
q: The central humidifier is running.
r: The air in the house is getting dry.

5. p: The ouside humidity is high.
q: The basement dehumidifier is running.
r: The basement is getting moldy.

Let p, q, and r represent the following simple statements.
P: There is a blizzard outside.
q: We do not have to go to school.
r: We go sledding.
First place parenthesis as needed before and after the most dominant connective and then translate the symbolic statement into English.

1. ~r-(this is an arrow) ~p v~q

2. r---p ^q( this is an arrow pointing toward r and p)

Solution Preview

Give that p and q each represent a simple statement, write the indicated compound statement in its symbolic form.

1.p: This is a hammer
q: This is a tool.
If this is not a hammer , then this is not a tool.

~P --> ~Q

2. p: The cone has three scoops .
q. The cone costs $1.85.
The cone has three scoops if and only if the cone costs ...